3,920 research outputs found
Upper Bound on the Capacity of a Cascade of Nonlinear and Noisy Channels
An upper bound on the capacity of a cascade of nonlinear and noisy channels
is presented. The cascade mimics the split-step Fourier method for computing
waveform propagation governed by the stochastic generalized nonlinear
Schroedinger equation. It is shown that the spectral efficiency of the cascade
is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The
results may be applied to optical fiber channels. However, the definition of
bandwidth is subtle and leaves open interpretations of the bound. Some of these
interpretations are discussed.Comment: The main change is to define the noise as bandlimited already in (8)
rather than before (15). This serves to clarify subsequent step
Stabilization of Linear Systems Over Gaussian Networks
The problem of remotely stabilizing a noisy linear time invariant plant over
a Gaussian relay network is addressed. The network is comprised of a sensor
node, a group of relay nodes and a remote controller. The sensor and the relay
nodes operate subject to an average transmit power constraint and they can
cooperate to communicate the observations of the plant's state to the remote
controller. The communication links between all nodes are modeled as Gaussian
channels. Necessary as well as sufficient conditions for mean-square
stabilization over various network topologies are derived. The sufficient
conditions are in general obtained using delay-free linear policies and the
necessary conditions are obtained using information theoretic tools. Different
settings where linear policies are optimal, asymptotically optimal (in certain
parameters of the system) and suboptimal have been identified. For the case
with noisy multi-dimensional sources controlled over scalar channels, it is
shown that linear time varying policies lead to minimum capacity requirements,
meeting the fundamental lower bound. For the case with noiseless sources and
parallel channels, non-linear policies which meet the lower bound have been
identified
Why compensating fibre nonlinearity will never meet capacity demands
Current research efforts are focussed on overcoming the apparent limits of
communication in single mode optical fibre resulting from distortion due to
fibre nonlinearity. It has been experimentally demonstrated that this Kerr
nonlinearity limit is not a fundamental limit; thus it is pertinent to review
where the fundamental limits of optical communications lie, and direct future
research on this basis. This paper details recently presented results. The work
herein briefly reviews the intrinsic limits of optical communication over
standard single mode optical fibre (SMF), and shows that the empirical limits
of silica fibre power handling and transceiver design both introduce a
practical upper bound to the capacity of communication using SMF, on the order
of 1 Pbit/s. Transmission rates exceeding 1 Pbit/s are shown to be possible,
however, with currently available optical fibres, attempts to transmit beyond
this rate by simply increasing optical power will lead to an asymptotically
zero fractional increase in capacity.Comment: 4 pages, 2 figure
Non-parametric Estimation of Mutual Information with Application to Nonlinear Optical Fibers
This paper compares and evaluates a set of non-parametric mutual information
estimators with the goal of providing a novel toolset to progress in the
analysis of the capacity of the nonlinear optical channel, which is currently
an open problem. In the first part of the paper, the methods of the study are
presented. The second part details their application to several
optically-related channels to highlight their features.Comment: This work has been submited to IEEE International Symposium on
Information Theor
Improved Lower Bounds on Mutual Information Accounting for Nonlinear Signal-Noise Interaction
In fiber-optic communications, evaluation of mutual information (MI) is still
an open issue due to the unavailability of an exact and mathematically
tractable channel model. Traditionally, lower bounds on MI are computed by
approximating the (original) channel with an auxiliary forward channel. In this
paper, lower bounds are computed using an auxiliary backward channel, which has
not been previously considered in the context of fiber-optic communications.
Distributions obtained through two variations of the stochastic digital
backpropagation (SDBP) algorithm are used as auxiliary backward channels and
these bounds are compared with bounds obtained through the conventional digital
backpropagation (DBP). Through simulations, higher information rates were
achieved with SDBP, {which can be explained by the ability of SDBP to account
for nonlinear signal--noise interactionsComment: 8 pages, 5 figures, accepted for publication in Journal of Lightwave
Technolog
Bounds on the Per-Sample Capacity of Zero-Dispersion Simplified Fiber-Optical Channel Models
A number of simplified models, based on perturbation theory, have been
proposed for the fiber-optical channel and have been extensively used in the
literature. Although these models are mainly developed for the low-power
regime, they are used at moderate or high powers as well. It remains unclear to
what extent the capacity of these models is affected by the simplifying
assumptions under which they are derived. In this paper, we consider single
channel data transmission based on three continuous-time optical models i) a
regular perturbative channel, ii) a logarithmic perturbative channel, and iii)
the stochastic nonlinear Schr\"odinger (NLS) channel. We apply two simplifying
assumptions on these channels to obtain analytically tractable discrete-time
models. Namely, we neglect the channel memory (fiber dispersion) and we use a
sampling receiver. These assumptions bring into question the physical relevance
of the models studied in the paper. Therefore, the results should be viewed as
a first step toward analyzing more realistic channels. We investigate the
per-sample capacity of the simplified discrete-time models. Specifically, i) we
establish tight bounds on the capacity of the regular perturbative channel; ii)
we obtain the capacity of the logarithmic perturbative channel; and iii) we
present a novel upper bound on the capacity of the zero-dispersion NLS channel.
Our results illustrate that the capacity of these models departs from each
other at high powers because these models yield different capacity pre-logs.
Since all three models are based on the same physical channel, our results
highlight that care must be exercised in using simplified channel models in the
high-power regime
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